Sr Examen

Derivada de x×sin1/x+arcsinx/arccosx

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
x*sin(1)   asin(x)
-------- + -------
   x       acos(x)
$$\frac{\operatorname{asin}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} + \frac{x \sin{\left(1 \right)}}{x}$$
(x*sin(1))/x + asin(x)/acos(x)
Gráfica
Primera derivada [src]
         1                  asin(x)       
------------------- + --------------------
   ________              ________         
  /      2              /      2      2   
\/  1 - x  *acos(x)   \/  1 - x  *acos (x)
$$\frac{1}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{\operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}$$
Segunda derivada [src]
     x                2               2*asin(x)             x*asin(x)     
----------- - ----------------- - ------------------ + -------------------
        3/2   /      2\           /      2\     2              3/2        
/     2\      \-1 + x /*acos(x)   \-1 + x /*acos (x)   /     2\           
\1 - x /                                               \1 - x /   *acos(x)
--------------------------------------------------------------------------
                                 acos(x)                                  
$$\frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{x \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}} - \frac{2 \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right) \operatorname{acos}^{2}{\left(x \right)}}}{\operatorname{acos}{\left(x \right)}}$$
Tercera derivada [src]
                     2                                                                                                      2                                 
     1            3*x                6                   asin(x)                6*x                6*asin(x)             3*x *asin(x)          6*x*asin(x)    
----------- + ----------- + -------------------- + ------------------- + ------------------ + -------------------- + ------------------- + -------------------
        3/2           5/2           3/2                    3/2                    2                   3/2                    5/2                    2         
/     2\      /     2\      /     2\        2      /     2\              /      2\            /     2\        3      /     2\              /      2\      2   
\1 - x /      \1 - x /      \1 - x /   *acos (x)   \1 - x /   *acos(x)   \-1 + x / *acos(x)   \1 - x /   *acos (x)   \1 - x /   *acos(x)   \-1 + x / *acos (x)
--------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                           acos(x)                                                                            
$$\frac{\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(x \right)}} + \frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}{\left(x \right)}} + \frac{6 x \operatorname{asin}{\left(x \right)}}{\left(x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(x \right)}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(x \right)}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \right)}} + \frac{6 \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(x \right)}}}{\operatorname{acos}{\left(x \right)}}$$
Gráfico
Derivada de x×sin1/x+arcsinx/arccosx